BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter F, Problem 42E
To determine

To prove: The generalized triangle inequality |i=1nai|i=1n|ai|.

Expert Solution

Explanation of Solution

Compute summing of the inequalities |ai|ai|ai| for i=1,2,,n.

i=1n|ai|i=1naii=1n|ai| (1)

It is known that if |x|c iff cxc.

So, equation (1) can be written as, |i=1nai|i=1n|ai|.

Hence the formula is proved.

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